In the field of the braking control for a vehicle, such as an automobile, it has been proposed to perform a braking force assist control (brake assist control) which increases a braking force applied to a vehicle in comparison with that in a usual braking operation when a possibility of a collision of the vehicle is detected. In a system which executes such a braking force assist control when a possibility of a collision of a vehicle is detected, a braking force at a level adequate and agreeable for a driver is applied in a usual braking operation. However, when a possibility of a collision of the vehicle is detected, a braking force larger than usual is applied so that the deceleration of the vehicle will be more ensured for achieving the avoidance of the collision. As an example of performing such a braking force assist control in response to the detection of a possibility of a collision of a vehicle, for instance, patent document 1 discloses a braking control in which a braking force assist is conducted in a brake mechanism when the performing of an urgent depressing operation is detected based on the depression amount and depression velocity of a brake pedal. In this example, when a necessity of a collision avoidance operation is detected based on the distance and relative velocity between the own vehicle and an obstruction, the intervention of the braking force assist is performed in response to the lighting of a stop lamp, and the detection reference value for an urgent depressing operation is lowered in proportion to the increase of the detected collision possibility. Further, patent document 2 proposes a device which controls a braking force for a contact avoidance support based on a target velocity computed according to the distance of an obstacle from a vehicle front, wherein the target velocity is made higher for making the rising of the braking force slower during steering operation, thereby preventing the interference between the automatic braking and the driver's voluntary contact avoidance operation and dissolving the driver's sense of incongruity.